A Study of Orthogonal Matrix-valued Multivariate Wavelet Packets Associated with a Dilation Matrix

Author

Lu, Jun ; Li, Tizheng

Author_Institution

Dept. of Math., Zhengzhou Teachers´´ Coll., Zhengzhou, China

Volume

4

fYear

2009

fDate

19-21 May 2009

Firstpage

360

Lastpage

363

Abstract

The notion of matrix-valued multiresolution analysis of space L²(R³,C^rtimesr) is introduced. An approach for constructing orthogonal matrix-valued higher-dimensional wavelet packets is presented and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Finally, one new orthonormal basis of L²(R³,C^rtimesr) is obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

Keywords

functional analysis; matrix algebra; time-frequency analysis; wavelet transforms; dilation matrix; functional analysis method; higher-dimensional wavelet packet; matrix theory; matrix-valued multiresolution analysis; orthogonal matrix-valued multivariate wavelet packet; time-frequency analysis method; Educational institutions; Functional analysis; Intelligent systems; Mathematics; Multidimensional systems; Multiresolution analysis; Time frequency analysis; Wavelet analysis; Wavelet packets; Wavelet transforms; higher-dimensional; matrix-valued; orthonormal basis; wavelet packets;

fLanguage

English

Publisher

ieee

Conference_Titel

Intelligent Systems, 2009. GCIS '09. WRI Global Congress on

Conference_Location

Xiamen

Print_ISBN

978-0-7695-3571-5

Type

conf

DOI

10.1109/GCIS.2009.401

Filename

5209271